Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
568 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C52×#97 | C2 | semidirect |
| 4. C8×#1039 | C2 | semidirect |
| 5. #11716670 | C2 | semidirect |
| 13. #87799 | C4 | semidirect |
| 22. C52×C8 | C2×C4 | semidirect |
| 23. #6029 | C2×C4 | semidirect |
| 26. C5×#97 | D5 | semidirect |
| 35. #1039 | M16 | semidirect |
| 55. C5×C8 | C4×D5 | semidirect |
| 60. #97 | C5⋊D5 | semidirect |
| 62. C52 | C4×M16 | semidirect |
| 89. C8 | C4×C5⋊D5 | semidirect |
| 90. C5 | #64996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87799 | 2 |
| C42×C5⋊D5 | 2 |
| C52×#97 | 2 |
| C8×#1039 | 2 |
| #11716670 | 2 |
| #64996 | 5 |